几个有限三角和
A Few Finite Trigonometric Sums
摘要：
有限三角和出现在物理、数学及其应用的各个分支中。这些和可以包含一个或多个三角函数的各种幂。已知具有一个三角函数的和，然而具有三角函数的乘积的和可能变得复杂，并且在许多情况下可能不具有简单的表达式。其中一些和具有有趣的性质，并且可以具有令人惊讶的简单值。然而，其中只有一些是在文献中。我们利用留数法得到了一些这样的和。
英文摘要：
Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known, however sums with products of trigonometric functions can get complicated and may not have a simple expressions in a number of cases. Some of these sums have interesting properties and can have amazingly simple value. However, only some of them are available in literature. We obtain a number of such sums using method of residues.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
